Integrating packing and distribution problems and optimization through mathematical programming

Abstract

This paper analyzes the integration of two combinatorial problems that frequently arise in production and distribution systems. One is the Bin Packing Problem (BPP) problem, which involves finding an ordering of some objects of different volumes to be packed into the minimal number of containers of the same or different size. An optimal solution to this NP-Hard problem can be approximated by means of meta-heuristic methods. On the other hand, we consider the Capacitated Vehicle Routing Problem with Time Windows (CVRPTW), which is a variant of the Travelling Salesman Problem (again a NP-Hard problem) with extra constraints. Here we model those two problems in a single framework and use an evolutionary meta-heuristics to solve them jointly. Furthermore, we use data from a real world company as a test-bed for the method introduced here.